The kidnappers claimed an air and ground assault on the In Amenas gas complex had left 34 hostages dead.

The militants said 15 of their number were also killed.

A foreign diplomat in Algiers confirmed the rescue mission "did not go too well for the hostages".

Abu al-Baraa ... reported to have been killed in the raid. Photo: AFP

According to the Mauritanian news site al-Akhbar, Baraa was "one of the most important chiefs of the Mokhtar Belmokhtar brigade".

Al-Akbar said Baraa was also "probably of Algerian nationality," and said he was born in the late 1970s and became a member of the Salafist Group for Preaching and Combat (GSPC).

The Algerian government said it was forced to intervene due to the militants' stubbornness and their desire to escape with the hostages.

"An important number of hostages were freed and an important number of terrorists were eliminated, and we regret the few dead and wounded," Algerian Communications Minister Mohand Said Oubelaid told media, adding that the "terrorists are multinational," coming from several different countries with the goal of "destabilising Algeria, embroiling it in the Mali conflict and damaging its natural gas infrastructure".

Algerian Interior Minister Dahou Ould Kablia said the militants came from Libya.

"According to the information we have, the terrorist group which attacked the In Amenas site came from Libya," Kablia told the online edition of Algerian daily Echorouk.

Kablia had on Wednesday said that the kidnappers were from the region, denying that they came from Libya, or from Mali as some of them claimed.

The militants - reportedly led by the veteran jihadist Mokhtar Belmokhtar - had previously threatened to "eliminate" the hostages if they were attacked.

Norwegian Prime Minister Jens Stoltenberg would not criticise the Algerian operation but said he wished the Norwegian government would have been notified before it started.

He added that while Algeria has declined medical help, Norway will send a plane with medical equipment and personnel.

An unarmed US surveillance drone soared overhead as the Algerian forces closed in, US officials told the Associated Press.

The US offered military assistance to help rescue the hostages - whose numbers varied wildly from dozens to hundreds - but the Algerian government refused, a US official said in Washington DC, speaking on condition of anonymity.

British offers of assistance to Algeria in dealing with the situation were also declined.

British Prime Minister David Cameron was told the operation was under way only when he telephoned the Algerian prime minister at 1130 GMT (2230 AEDT).

Cameron made clear that he would have preferred to be informed in advance, but the Algerians said they had to act "immediately".

UK Foreign Office Minister Alistair Burt said: "Although details have yet to become final, I am afraid we should be under no illusion that there will be some bad and distressing news to follow from this terrorist attack".